The Mathematical Symbol "There Does Not Exist (∄)"

The ∄ Symbol in Logic: "There Does Not Exist"

The ∄ symbol, pronounced as "there does not exist", is crucial in mathematical logic and set theory. It represents the negation of existential quantification. Essentially, it communicates that within a specified domain, no element satisfies a particular property or condition. This article sheds light on its interpretation and provides two illustrative examples.


In the realms of logic and mathematics, the ∄ symbol is utilized to express the absence of any element that meets a given criterion. When paired with a variable and a proposition, it negates the existence of any instance where the proposition is true for that variable.


  • Example 1: Mathematical Statement:
    If we wish to convey that there's no real number \( x \) such that \( x^2 = -1 \), it can be notated as:
    ∄ \( x \) in ℝ : \( x^2 = -1 \). In this instance, the statement is true because the square of any real number cannot be negative.
  • Example 2: Set Theory:
    To assert that a set \( S \) doesn't have any even prime numbers apart from 2, one can write:
    ∄ \( n \) in \( S \) (where \( n > 2 \)) : \( n \) is an even prime. This statement confirms the unique nature of 2 as the only even prime number.

To wrap up, the ∄ symbol is invaluable in mathematical expressions. It allows for the precise negation of the existence of elements with certain properties within a designated domain. Like its counterpart, ∃, it exemplifies the meticulous nature of mathematical language.

Mathematical symbol 'There Does Not Exist'

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Codes for the ∄ Symbol

The Symbol
Alt CodeAlt 8708
HTML Code∄
HTML Entity∄
CSS Code\2204
Hex Code∄

How To Insert the ∄ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ∄ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8708. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8708;</b>My symbol: ∄

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &nexist;</b>My symbol: ∄

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\2204";}
<span>My symbol:</span>
My symbol: ∄

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x2204;</b>My symbol: ∄
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x2204 to place the ∄ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ∄ is U+2204. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 2204 turns into ∄. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u2204. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u2204"
document.write("My symbol: " + str)
My symbol: ∄